Introduction to Quantum Mechanics · Problem 4.7

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · spherical_harmonics_construction

Problem

Using Equation 4.32, find

Y_\ell^\ell(\theta, \phi)

and

Y_3^2(\theta, \phi)

. (You can take

P_3^2

from Table 4.2, but you'll have to work out

P_\ell^\ell

from Equations 4.27 and 4.28.) Check that they satisfy the angular equation (Equation 4.18), for the appropriate values of

\ell

and

m